A classical computer operates by processing binary bits of information that change state according to the laws of classical physics. These information bits can be modified by using simple logic gates such as AND and OR gates. The binary bits are physically created by a high or a low signal level occurring at the output of the logic gate to represent either a logical one (e.g., high voltage) or a logical zero (e.g., low voltage). A classical algorithm, such as one that multiplies two integers, can be decomposed into a long string of these simple logic gates. Like a classical computer, a quantum computer also has bits and gates. Instead of using logical ones and zeroes, a quantum bit (“qubit”) uses quantum mechanics to occupy both possibilities simultaneously. This ability and other uniquely quantum mechanical features enable a quantum computer can solve certain problems exponentially faster than that of a classical computer.
Quantum annealing starts from a quantum-mechanical superposition of all possible states, referred to as candidate states) with equal weights. The system evolves following the time-dependent Schrödinger equation, a natural quantum-mechanical evolution of physical systems. The amplitudes of all candidate states keep changing, realizing a quantum parallelism, according to the time-dependent strength of the transverse field, which causes quantum tunneling between states. If the rate of change of the transverse-field is slow enough, the system stays close to the ground state of the instantaneous Hamiltonian. If the rate of change of the transverse-field is accelerated, the system may leave the ground state temporarily but produce a higher likelihood of concluding in the ground state of the final problem Hamiltonian. The transverse field is switched off, and the system is expected to have reached the ground state or otherwise computationally useful state of the classical lsing model that corresponds to a solution or approximate solution to the original optimization problem.